Once upon a time, and old lady went to sell her vast quantity of eggs at the local market.
When asked how many she had, she replied:
Son, I can't count past 100 but I know that.
If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be one egg left.
If you divide the number of eggs by 4 there will be one egg left.
If you divide the number of eggs by 5 there will be one egg left.
If you divide the number of eggs by 6 there will be one egg left.
If you divide the number of eggs by 7 there will be one egg left.
If you divide the number of eggs by 8 there will be one egg left.
If you divide the number of eggs by 9 there will be one egg left.
If you divide the number of eggs by 10 there will be one egg left.
Finally. If you divide the number of eggs by 11 there will be NO EGGS left!
How many eggs did the old lady have?
HINT #1
Spoiler:
HINT #2
Spoiler:
ANSWERSpoiler:
We know that where .
Also, all number's that when divided by that leaves 1 as a remainder are of the form
where .
This sets up a diophantine equation
whose solution is
so as previous stated with the minimum being when .
Just thought I'd put some details in.